A method has been developed for in-room computer reconstruction of the three-dimensional (3-D) coronary arterial tree from routine biplane angiograms acquired at arbitrary angles and without using calibration objects. The proposed method consists of four major steps: (1) segmentation of vessel centerlines and bifurcation points and measurement of vessel diameters in coronary angiograms, (2) determination of biplane imaging parameters in terms of a rotation matrix R and a translation vector t based on the identified bifurcation points, (3) recovery of 3-D coronary arterial tree based on the calculated biplane imaging parameters, correspondences of vessel centerlines, and diameters, and (4) rendering of reconstructed 3-D coronary tree and estimation of optimal view of selected arterial segments. Angiograms from fifteen patients were utilized for 3-D reconstruction for each patient's coronary arterial tree. The biplane imaging geometry was first determined without a calibration object, and the 3-D coronary arterial trees were reconstructed including both left and right coronary artery systems. Various 2-D projection images of the reconstructed 3-D coronary arterial tree were generated and compared to other viewing angles obtained in the actual patient study. Similarity between the real and reconstructed arterial structures was excellent. The accuracy of this method was evaluated by using a computer-simulated coronary arterial tree. Root-mean-square (RMS) errors in the 3-D position and 3-D configuration of vessel centerlines and in the angles defining the R matrix and $t vector were 1.2 - 5.5 mm, 0.3 - 2.0 mm, and less than 1.5 and 2.0 degrees, respectively, when using 2-D vessel centerlines with RMS normally distributed errors varying from 0.7 - 4.2 pixels (0.25 - 1.26 mm).